Apparatus for playing a mathematical board game



Aug. 12, 1969 o. E. CRANS 3,460,835

APPARATUS FOR PLAYING A MATHEMATICAL BOARD GAME Filed Aug- 22. 1966 2Sheets-Sheet 1 24 nun wu sconms mm. POINTS no-n4 ITS-I80 s I65-l69lBl-IBS 4 160-164 use-I90 3 459 I9l-l95 --2 :54 I96-200 INVENTOR. DAVIDE. CRANS FIG.3 (P A UNDER I50 0R OVER 200"--O Filed Aug! 22 1966 Aug.12, 1969 I v o. E. CRANS v 3,460,835

APPARATUS FOR PLAYING A MATHEMATICAL BOARD 0AM]:

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' INVENTOR. DAVID E. CRA NS 'r'ron EYS 3,460,835 APPARATUS FOR PLAYING AMATHEMATICAL BOARD GAME David E. Crans, 1149 N. Old Manor, Wichita,Kans. 67208 Filed Aug. 22, 1966, Ser. No. 573,942 Int. Cl. A63f 3/00,9/06 US. Cl. 273135 3 Claims ABSTRACT OF THE DISCLOSURE Various types ofnumerical games are known to the prior art using a plurality of numberedpieces selectively placed on a given game board in a certain order toindicate ones skill. However, the prior art devices are used in a mannerto indicate ones skill in multiplication, subtraction, or the like andare not operable in a manner requiring one to foresee innumerablecombinations of present and future plays to pit one players skillagainst anothers similar to a game of chess.

In preferred specific embodiments of the invention, a mathematical gameis provided for play by two persons having a game board, a plurality ofnumbered pieces, and rack members to hold the pieces so as to be readilyvisible to the respective players. The game board has a plurality ofintersecting horizontally and vertically disposed rows of square spacessimilar to a checker board. A plurality of consecutively numbered gamepieces are provided which are placed according to the rules of the gameon individual ones of the spaces in calculated order by the respectiveplayers. The pieces can be placed on the racks as drawn from a pile soas to be readily visible to each player, respectively, and providing aplurality of choices of the pieces prior to play upon the spaces in amanner as set forth in the rules of play. After covering all of thespaces with the pieces, the winner is determined by adding therespective sums of each vertical and horizontal row and the player withthe highest bonus score determined by minimum deviation of his set ofrows from a predetermined sum is the winner. It is seen that the gameinvolves mental skill in applying a numbered piece to a given space, asfor example, in a horizontal row so as to approach a predetermined sumwithout aiding the opponent in obtaining this sum in his vertical row towhich the space is common.

Accordingly, an object of this invention is to provide a new and novelnumerical game that is educational and challenging.

Another object of this invention is to provide a numerical game that isplayed by two persons in a test of relative skill.

Still another object of this invention is to provide a numerical gamewhich is interesting to play and aids in teaching one rapid addition.

Still one other object of this invention is to provide a numerical gamethat is simple and easy to understand and provides a challenging battleof player skill.

A further object of this invention is to provide a game apparatus havinga plurality of vertical and horizontal knited States Patent PatentedAug. 12, 1969 rows of spaces and an equal amount of numbered piecesplaced in selected positions in the spaces to arrive at a predeterminednumerical sum in each of the vertical .and horizontal rows,respectively, whereupon the player nearest to the predeterminednumerical sum in most of the rows is declared the winner.

One further object of this invention is to provide a game apparatus thatis economical to manufacture, simple to understand, and presents achallenging game that evaluates ones mathematical and thinking skill.

Various other objects, advantages and features of the invention willbecome apparent to those skilled in the art from the followingdiscussion, taken in conjunction with the accompanying drawings inwhich:

FIG. 1 is a perspective view of the mathematical game of this inventionillustrated as mounted upon a playing table in the normal position ofplay;

FIG. 2 is an enlarged top plan view of a game board and a sheet ofnumbered pieces of the mathematical game of this invention;

FIG. 3 is an enlarged plan view of the scoring portion of the game boardof the mathematical game of this invention;

FIG. 4 is a top plan view of the game board and the separated numberedpieces of the mathematical game of this invention similar to FIG. 2illustrating the same during an intermediate stage of game play; and

FIG. 5 is a top plan view similar to FIG. 4 illustrating a completedstage of the mathematical game of this invention.

The following is a discussion and description of preferred specificembodiments of the new mathematical game of this invention, such beingmade with reference to the drawings, whereon the same reference numeralsare used to indicate the same or similar parts and/or structure. It isto be understood that such discussion and description is not to undulylimit the scope of the invention.

Referring to the drawings in detail, and particularly to FIG. 1, themathematical game of this invention, indicated generally at 12, is shownon a conventional table 13 in the proper position of play. Themathematical game 12 is known as Double Cross and includes a largesquare game board 15, a sheet 17 of consecutively numbered game pieces18, and a pair of rack members 20 used to hold the pieces 18 of eachrespective player.

As shown in FIG. 2, the game board 15 has an inner square playingsection 21 comprised of a plurality of spaces 23 separated by strips 24.The playing section 21 has its corners adjacent mid-portions of sides 26of the game board 15 thereby placing the diagonals thereof perpendicularto the sides 26. The spaces 23 are arranged in horizontally andvertically disposed rows 28 and 29, respectively, of seven each andidentified by consecutive numerals 31 within triangular-shaped bordersections 33. The numerals 31 are positioned so as to be readily readableby the opposed players to identify the horizontal and vertical rows 28and 29, respectively, being played by the individual players. The nameof the game Double Cross is placed in diagonally opposed corners of thegame board 15 with the other corners having scoring tables 35 therein.As shown in FIG. 3, each table 35 has a. heading Scoring and a numericaltotal column and a credit or bonus points column. In this particularpreferred embodiment of the invention, a mathematical total of 175 isconsidered a perfect score and given bonus points equal to a numericaltotal of 10 with deviations above or below this predetermined sum givena smaller number of bonus points until below or above 200 is given nocredit. The application of the scoring table 35 in playing the game willbecome obvious.

The sheet 17 is perforated so as to be readily separable into the pieces18 of equal size adaptable to individually cover a selected one of thespaces 23 during play of the mathematical game 12. The pieces 18 arenumbered consecutively from 1 to 49 having the numerals thereon extendedparallel to one diagonal of the square pieces 18 for reasons to beexplained.

As shown in FIG. 1, the rack members 20 are of L shape in transversecross-section and adapted to be placed in front of each respectiveplayer to hold the pieces 18 during play of the mathematical game 12.The rack members 20 are merely convenient tools to hold the pieces 18 soas to be visible only to the player using the same.

Additionally, the mathematical game 12 is supplied with a book orpamphlet entitled Double CrossRules of Play setting forth in detail theguide lines and steps of how to set up, score, and play the game. First,Double Cross is a game played by two persons having to deal with theplacement of the forty-nine pieces 18 on the same number of spaces 23 onthe game board 15. One player uses the vertical rows 29 and the otherplayer the horizontal rows 28 with a total of the numbered pieces 18 ineach individual row to approach the perfect or predetermined sum of 175.Therefore, the object of the game 12 is for each player by the end ofplay to make his rows individually add to 175 or as close as possibleand, at the same time, try to prevent his opponents rows from adding upto the 175 total.

In the operation and play of the mathematical game 12, the numericalpieces 18 are placed face down on the table 13 and mixed up whereuponeach player draws one of the pieces 18 and the highest numbered oneplays first. The drawn numerical pieces 18 are placed back into thepile, again face down, mixed up, and then each player draws seven newpieces 18 and places them on his respective rack member 20.

The first player then starts off by placing one of his seven pieces 18on the central one of the spaces 23 indicated generally at 38 (FIG. 2).This player then replaces the played piece 18 by drawing from the pileof pieces 18, and the second player thereupon places one of his sevenoriginal pieces 18 on a selected one of the spaces 23. This piece 18played by the second player from his rack member 20 is then replaced bydrawing from the pile as previously described for the first player andthe players continue to alternate in this manner of play until all thepieces 18 are placed on the spaces 23. After the first play on thecenter space 38, the numbered pieces 18 may be placed on any of thespaces 23 but, once played thereon, -a piece cannot be moved. It is seenthat the pieces 18 are placed on the game board so as to be facing in acommon lateral direction relative to the players and, therefore, arereadily visible to both.

In order to facilitate the play, upon placing the fourth, fifth, sixthor seventh numbered piece 18 in any of the rows 28 and 29, the playermust announce the new total for that row. If the played piece 18 is thefourth, fifth, sixth or seventh one of the numbered pieces 18 in both ofthe two crossing rows 28 and 29, the player must now announce both ofthese new totals. Additionally, as soon as there are four pieces 18 in agiven row 28 or 29 being played, the player keeps a running total ofthat row on a score pad or the like until it is filled. It is obviousthat this procedure is necessary to eliminate the need for adding eachrow over and over before playing a piece 18 therein.

As shown in FIG. 4, during an intermediate stage of play, the playersare facing each other with one playing the horizontal rows 28 and theother the vertical rows 29. As an example of the numerical sumannouncement procedure, if the piece 18 numbered 13 is now played, theplayer announces 84 and 90 which indicates, first, the scoring of hisrespective vertical row 29 and, secondly, the opponents score in hishorizontal row 28. It is seen that this is required as the piece 18numbered 13 is the fourth one placed in the vertical row and the fifthone placed in the horizontal row.

On completing the game play as shown in FIG. 5, each player totals hisrespective rows 28 and 29 and converts his score to the bonus points asshown in the tables 35. For example, a player of the vertical rows 29has scores of l83-202-143l76164-165-192, which, when converted to bonuspoints equals 4-0-0534-2, respec tively, for a grand total score of 18.Similarly, the other player has scores for the horizontal rows 28 of193-190- 185170-171-15l165 for bonus points of 23-4 55- 14 for a grandtotal of 24. It is seen, therefore, that the horizontal row player hasexhibited more skill in arriving at the largest grand total of bonuspoints and is declared the winner.

The average game played will normally consume 30 to 40 minutes and thescore will range from 10 to 25 points depending on the relative score ofthe players with scores below and above this range indicative of poorand excellent play, respectively. It is obvious that the players engagein mental combat in attempting to arrive at the total of for each of therespective rows, while, at the same time, attempting to place theopponents rows at a sum as far removed from 175 as possible. Therefore,numerous combinations of plays are available requiring mental skill inforeseeing future plays in light of the pieces available to each player.

The game board of the invention has been illustrated with seven each ofhorizontal and vertical rows resulting in 49 spaces and pieces numberedconsecutively from 1 to 49, inclusive. In this preferred embodiment, itis seen that the numerical total of the pieces is 1,225, exactly equalto 7 times 175 (the ideal score), whereby it is possible, howeverextremely unlikely, for a player to have all seven respective row scoresequal to the predetermined ideal sum of 175.

Although the mathematical game is described for seven rows in thehorizontal and vertical, the number of rows can be altered to change thedegree of difliculty of the Double Cross game with the only major changebeing the determination of a new predetermined sum. This perfect averageor sum can be readily determined by the following formula:

or, equally; wherein:

PS=perfect score N=number of horizontal or vertical rows It is seen thatfor a simpler six row game, the perfect sum would be:

and the pieces would be numbered from 13 6, to be placed according tothe previously described Double Cross- Rules of Play on thecorresponding 36 spaces.

As will be apparent from the foregoing description of the preferredembodiments of applicants mathematical game, a relatively simple andeasy to understand game has been provided to test ones mental abilitysimilar to the commonly known chess game.

While the invention has been described in connection with preferredspecific embodiments thereof, it is to be understood that thisdescription is intended to illustrate and not to limit the scope of theinvention, which is defined by the following claims.

I claim:

1. An apparatus for playing a mathematical game requiring at least twoplayers, comprising:

(a) a rectangular game board having a plurality of intersectinggenerally vertically and horizontally disposed rows of rectangularspaces, the rows being of equal number both vertically and horizontally,each space being common to one vertical row and one horizontal row,

square pieces beginning with numeral 1 and extending through the numeralwhich is the square of the number of vertical rows, each piece being thesame (b) a plurality of consecutively numerically marked rectangularpieces beginning with numeral 1 and 5 extending through the numeralwhich is the square of the number of either vertical or horizontal rows,each piece selectively positionable within one of said spaces wherebythe numerical sum of said pieces in each roW may equal a predeterminedvalue and 10 any deviation therefrom may serve as an indication ofrelative player skill, said numerals on said pieces being positionedthereon so as to be upright when viewed along a diagonal of the piece,and

(c) the diagonals of said spaces extending perpendicu- 5 lar torespective sides of said game board so that size as each of the otherpieces and selectively positionable within one of said spaces wherebythe numerical sum of said pieces in each row may equal a predeterminedsum and any deviation therefrom may serve as an indication of relativeplayer skill,

(c) said numerals on said pieces being positioned thereon so as to beupright When viewed along a diagonal of a piece, and

(d) the diagonals of said spaces extending perpendicular to respectivesides of the game board.

References Cited UNITED STATES PATENTS the indicia on said pieces arereadily readable by 2,399,902 5 /1946 Wood both Playera 300,534 6/1884Van Bibber. 2. A game apparatus as described in claim 1, wherein 1 457333 1923 il said game board has scoring indicia on diagonally op-1,633,445 6/1927 G il r a1, posed corners facing adjacent respectiveplaying sides 2,170,909 8/1939 Moren, so as to be easily readable by thecorresponding players. 2,871,581 2/1959 Guzak 273l35 X 3. An apparatusfor playing a mathematical game requiring at least two players,comprising: FOREIGN PATENTS (a) a square game board having a pluralityof inter- 174,228 1/1922 Great Britain, secting generally vertically andhorizontally disposed 844,983 8/ 1960 Great Britain.

rows of square spaces of equal size, there being equal numbers ofvertical and horizontal rows, each space being common to one verticaland one horizontal row,

(b) a plurality of consecutively numerically marked DELBERT B. LOWE,Primary Examiner US. Cl. X.R.

